Question: The grades on a history midterm at Covington are normally distributed with $\mu = 70$ and $\sigma = 4.5$. Stephanie earned a $60$ on the exam. Find the z-score for Stephanie's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Stephanie's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{60 - {70}}{{4.5}}} $ ${ z \approx -2.22}$ The z-score is $-2.22$. In other words, Stephanie's score was $2.22$ standard deviations below the mean.